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Amaral, L.A.N., Plerou, V., Gopikrishnan, P., Meyer, M. and Stanley, H.E. (2000) The Distribution of Returns of Stock Prices. International Journal of Theoretical and Applied Finance, 3, 365-369.
https://doi.org/10.1142/s0219024900000218

has been cited by the following article:

• TITLE: Convolution Rather Than Monte Carlo Simulation to Price a Barrier Option

  AUTHORS: Daniel T. Cassidy

  KEYWORDS: Option Pricing, Convolution, Truncation, Student’s t Distribution, Fat Tails, S&P 500 Returns

  JOURNAL NAME: Journal of Mathematical Finance, Vol.15 No.3, August 18, 2025

  ABSTRACT: Repeated convolution and truncation of a truncated fat-tailed distribution, instead of Monte Carlo simulation, for pricing a discrete, simple barrier option is presented. The parameters for the truncated fat-tailed distribution are obtained by fitting the sum of a Student’s t distribution plus a normal distribution to the one-day returns obtained from the adjusted closing values for the S&P 500. It is argued that truncation of the fat-tailed, one-day returns distribution is a physically reasonable action and evidence to support this truncation is provided. The steps to price a discrete up-and-out barrier on an European call option through repeated convolution and truncation are given.